Quantitative Analysis: Acid-Base Titrations

Analysing Results: Concordancy and Mean Titre

The volume of liquid added from the burette is called the titre. It is calculated by subtracting the initial burette reading from the final burette reading.

During an experiment, the first run is usually a rough titre (or trial run). This is done quickly to find the approximate "drop zone" where the colour change happens. After this, precise drop-by-drop runs are performed to achieve concordant results — titre volumes that are strictly within $0.10 \text{ cm}^3$ of each other.

When calculating the mean titre, you must entirely exclude the rough titre and any anomalous results. You only ever average the concordant results.

Worked Example: Selecting Concordant Results

A student carries out a titration and records the following results. Calculate the mean titre.

Step 1: Identify the concordant results.

• Look for titres within $0.10 \text{ cm}^3$ of each other.
• Titre 2 ($23.30 \text{ cm}^3$) and Titre 3 ($23.40 \text{ cm}^3$) are concordant.
• The rough titre and Titre 1 are anomalies and must be ignored.

Step 2: Calculate the mean.

• $\text{Mean Titre} = \frac{23.30 + 23.40}{2} = 23.35 \text{ cm}^3$

Stoichiometry and Molar Ratios

Before calculating concentrations, you must know the reacting proportions of the acid and alkali. The fundamental ionic equation for neutralisation is always:

$\text{H}^+(aq) + \text{OH}^-(aq) \rightarrow \text{H}_2\text{O}(l)$

However, the full balanced chemical equation gives you the molar ratio — the ratio of the number of moles of each reactant required for complete neutralisation.

• 1:1 Ratio: One mole of hydrochloric acid neutralises one mole of sodium hydroxide ($\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}$).
• 1:2 Ratio: Sulfuric acid ($\text{H}_2\text{SO}_4$) contains two hydrogen ions per molecule, meaning one mole of sulfuric acid requires two moles of sodium hydroxide to neutralise ($\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}$).

Quantitative Analysis: Titration Calculations

To calculate the unknown concentration, you must always ensure your volumes are in $\text{dm}^3$. Convert from $\text{cm}^3$ to $\text{dm}^3$ by dividing by 1000.

The core formula used in these calculations is:

$\text{Moles} = \text{Concentration (mol/dm}^3) \times \text{Volume (dm}^3)$

Worked Example: A Complete Titration Calculation

$25.0 \text{ cm}^3$ of sodium hydroxide ($\text{NaOH}$) of unknown concentration was completely neutralised by $18.40 \text{ cm}^3$ of a $0.150 \text{ mol/dm}^3$ sulfuric acid ($\text{H}_2\text{SO}_4$) standard solution. Calculate the concentration of the sodium hydroxide in $\text{mol/dm}^3$.

The balanced equation is: $\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}$

Step 1: Calculate moles of the known reactant ($\text{H}_2\text{SO}_4$).

• Convert volume: $18.40 \div 1000 = 0.0184 \text{ dm}^3$

• $\text{Moles} = 0.150 \times 0.0184 = 0.00276 \text{ mol}$

Step 2: Use the balanced equation to find the molar ratio.

• The equation shows a 1:2 ratio ($\text{H}_2\text{SO}_4 : \text{NaOH}$).

• Therefore, moles of $\text{NaOH} = 0.00276 \times 2 = 0.00552 \text{ mol}$

Step 3: Calculate the unknown concentration.

• Convert volume: $25.0 \div 1000 = 0.025 \text{ dm}^3$

• $\text{Concentration} = \frac{\text{Moles}}{\text{Volume}} = \frac{0.00552}{0.025}$

• Answer: $0.221 \text{ mol/dm}^3$ (given to 3 significant figures)

Converting Between $\text{mol/dm}^3$ and $\text{g/dm}^3$ (Higher Tier)

Higher Tier students must be able to convert between two different measures of concentration: molar concentration (mol/dm³) and mass concentration (g/dm³).

The conversion factor between the two is the Relative Formula Mass ($M_r$) of the solute:

• To convert from mol/dm³ to g/dm³: Multiply by the $M_r$.
• To convert from g/dm³ to mol/dm³: Divide by the $M_r$.

Worked Example: Converting to Mass Concentration

Using the result from the previous calculation, find the concentration of the sodium hydroxide solution in $\text{g/dm}^3$. (Relative atomic masses: $Na = 23, O = 16, H = 1$)

Step 1: Calculate the $M_r$ of $\text{NaOH}$.

• $M_r = 23 + 16 + 1 = 40$

Step 2: Multiply the molar concentration by the $M_r$.

• $\text{Mass Concentration} = 0.2208 \text{ mol/dm}^3 \times 40$
• (Note: Use the unrounded value from your previous step to avoid rounding errors)
• Answer: $8.83 \text{ g/dm}^3$